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" If a body be acted on by a given force and revolve in a circle, the arc described .in any given time is a mean proportional between the diameter of the circle and the space through which a body would descend in the same time from rest if acted on by the... "
A Collection of Cambridge Mathematical Examination Papers: Papers in the ... - Page 139
by John Martin Frederick Wright - 1831
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The Mathematical Principles of Natural Philosophy, Volume 1

Sir Isaac Newton, John Machin - Celestial mechanics - 1729
...which a body, uniformly revolving in a circle by means of a given centripetal force, defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace which the fame body falling by the fame given force would defcend thro' in the .fame given time....
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The Laws of Centripetal and Centrifugal Force...

William Emerson - Medical - 1769 - 81 pages
...revolves uniformly in a circle, by means of a given centripetal force ; the arch which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace which the bod}' would defcend thro' in the fame time, and with the fame given force. For 2R (diameter)...
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Cyclomathesis: or, An easy introduction to the several branches of ..., Volume 7

William Emerson - Mathematics - 1769
...revolves uniformly in a circle, by means of a given centripetal force; the arch which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpacf which the body would defcend thro' in the fame time, and with the fame given force. For 2R (diameter)...
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Tracts: Containing: I. Mechanics, Or the Doctrine of Motion. II. The ...

William Emerson, William Bowe - Centrifugal force - 1793 - 302 pages
...uniformly in a circle, by means of a given centripetal force ; the arch -which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace -which the body would defcend through in the fame time, and -with the fame given force. For 2R...
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The Principles of Fluxions: Designed for the Use of Students in the University

Samuel Vince - Calculus - 1812 - 256 pages
...constant central force, will be increased in the same ratio of 1 : a2 ; therefore the arc described in any time is a mean proportional between the diameter of the circle and the distance fallen through in the same time, by the constant action of the centripetal force. Now the...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1819
...wh.ih a body uniformly revolving in a circle by means of a given centripetal force describes in any time, is a mean proportional between the diameter of the circle, and the space which the same body, lulling by the same gi .'en fo ce, would desceud thiou^h in the same given ti...
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A practical application of the principles of geometry to the mensuration of ...

Jeremiah Day - Measurement - 1815 - 96 pages
...equal to half radius. For the cosine of 60° is the sine of 30°. (Art. 89.) 97. The chord of any arc is a mean proportional, between the diameter of the circle, and the versed sine of the arc. Let ADB (Fig. 6.) be an arc, of which AB is the chord, BF the sine, and AF...
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New Series of The Mathematical Repository, Volume 4

Thomas Leybourn - Mathematics - 1819
...- a')' 7. The arc of a circle which a body, acted upon by a centripetal force, uniformly describes in any given time is a mean proportional between the diameter of the circle, and the space described by a heavy body from rest in the same time when urged by the force in the circumference continued...
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New series of The mathematical repository, Volume 4

Thomas Leybourn - Mathematics - 1819
...- 7, The аг-c of a> circle which. a body, acted u-ponby, a centripetal force, uniformly describes in any given time is a mean proportional between the diameter of the circle, andi the «pace described by a heavy body from rest in the same time when urged by the force in the...
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Cambridge Problems: Being a Collection of the Printed Questions Proposed to ...

Mathematics - 1821 - 425 pages
...of ~—, 7. The arc of a circle which a body, acted upon by a centripetal force, uniformly describes in any given time is a mean proportional between the diameter of the circle, and the space described by a heavy body from rest in the same time when urged by the force in the circumference continued...
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